What does tan 2pi equal?

##tan(2pi) =0##

In terms trigonometric functions, ##2pi## is equivalent to ##0##.

Based on the unit circle an angle of ##0## has its terminal point on the positive X-axis ; the side opposite the angle has a length of ##0## (and the adjacent side has a length of ##1##)

##tan = ("opposite")/("adjacent")##

##tan(2p) = tan(0) = 0/1 = 0##